Exercise (3): Open Channel Flow Rapidly Varied Flow

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Bryce Tate
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1 Exercise (3): Open Channel Flow Rapidly Varied Flow 1) A hydraulic jump exists in a trapezoidal channel having a bed width of 7 m and side slope of 1:1. The flowing discharge is 25 m 3 /sec. Construct the specific force diagram and get the two conjugate depths knowing that the height of the jump is 1 m. 2) The loss of energy head in a hydraulic jump formed in a rectangular channel is 4.25 m. The Froude number just before the jump is Find: a. The discharge per meter width of the channel b. The depths before and after the hydraulic jump c. Froude number after the jump d. Percentage loss of energy head due to jump e. Length of the jump 3) A hydraulic jump is to be formed in a trapezoidal channel with a base width of 7 m and side slope of 2:1. The downstream depth is 2.3 m and the discharge is 25 m 3 /sec. Find the upstream depth, the head lost and the horsepower dissipated in the jump. 4) A rectangular channel of 15 m bed width has a hydraulic jump which changes the depth of the stream from 1.2 m to 2.6 m. a. What is the flowing discharge? b. If a number of concrete blocks are placed in the floor to fix the position of the jump, what is the force on them for a downstream depth of 2.0 m (assuming the same discharge is flowing)? 5) A triangular channel whose top width is three times the water depth, n = passes a discharge of 3.32 m 3 /sec. Find the critical depth and the critical slope. If this discharge passes at a depth of 0.4 m, find the conjugate depth if a hydraulic jump takes place. Calculate also the HP lost through the jump. 6) The discharge through a 2 m wide rectangular channel is 6 m 3 /sec. If the head lost in a hydraulic jump is 3.5 m. Find the conjugate depths before and after the jump. 7) Construct the specific force diagram F for a flow of 12 m 3 /sec in a channel of triangular section with an apex angle of 90 o. A hydraulic jump is to be formed in the channel. Find the limiting value of the upstream depth if the downstream depth is not to exceed 3 m. Calculate the head lost and the horsepower dissipated in the jump. 8) A rectangular concrete channel 3.5 m wide carries 2.5 m 3 /sec in uniform flow. The slope is such that the velocity is double the velocity of critical flow. Find the slope assuming a constant Chezy coefficient of 50 (metric). To what height might the water jump and what will be the head lost in the jump? - 1 -

2 9) Water is flowing under the gate of a regulator. If the upstream depth is 5 m, the gate opening is 60 cm, and the D.S. depth of water away from the gate is 1.7m. a. Find the discharge flowing through the gate if its coefficient of discharge C d =0.60, and the coefficient of contraction C c = b. What will happen if the D.S. depth increases to 2.7 m without changing the depth upstream the gate? 10) Water discharges at a rate of 300 m 3 /sec over a spillway 14 m wide into a stilling basin of the same width. The lake level behind the spillway is 65 m above datum, and the river level downstream is 35 m above datum. Find the basic invert level required for a hydraulic jump to form within the basin. 11) Water flows under the gate of a regulator with coefficient of contraction Cc=0.65. If the downstream water depth away from the gate is 2.0m and water flows with a discharge of q=3.0 m 3 /s/m, find: a. The maximum gate opening (d) for the hydraulic jump to occur. b. The water depth upstream the gate assuming no head losses through the gate. c. Find the force on the gate in tons/m width of the gate. d. If the gate opening is reduced to d 2 =0.4m without affecting the discharge flowing through the canal. Find the water depth upstream the gate. e. If the gate opening is increased to d 3 =1.0m while keeping the flowing discharge the same, find the new force on the gate in tons/m width of the gate. Problems to be solved by computer: a) Create an Excel spread sheet that is able to calculate the following parameters in the hydraulic jump equation for the case of a trapezoidal channel section: a. Given Q, b, t, R, y 1 and required to get the value of y 2. b. Given Q, b, t, R, y 2 and required to get the value of y 1. c. Given Q, b, t, y 1, y 2 and required to get the value of R. The Excel sheet should be dynamic as much as possible. b) Water flows under the gate of a regulator with coefficient of contraction Cc. If the downstream water depth away from the gate is y 2 and water flows with a discharge of q m3/s/m, find using Excel: a. The maximum gate opening (d) for the hydraulic jump to occur. b. The water depth upstream the gate assuming no head losses through the gate. c. Find the force on the gate in tons/m width of the gate. Make your spread sheet dynamic in a way that it is able to solve the above requirements for any values of Q, b, y 2, and C c

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Exercise (4): Open Channel Flow - Gradually Varied Flow

Exercise (4): Open Channel Flow - Gradually Varied Flow 1) A wide channel consists of three long reaches and has two gates located midway of the first and last reaches. The bed slopes for the three reaches